Discrete spectrum of polynomially compact pseudodifferential operators and applications to the Neumann-Poincare operator in 3D elasticity

We present a new method for finding eigenvalue asymptotics for polynomially compact, zero order, pseudodifferential operators. As an application we find asymptotics of the spectrum of the Neumann-Poincare (double layer potential) integral operator of the 3D linear elasticity. We find relations of the geometrical characteristics of surface and the spectrum of the NP operator.